Write each of the following in scientific notation:
c. 0.37

Verified step by step guidance

1. Identify the given number: 0.37. Scientific notation expresses numbers as a product of a coefficient (between 1 and 10) and a power of 10.
2. Move the decimal point in the number 0.37 to the right until the coefficient is between 1 and 10. In this case, moving the decimal point one place to the right gives 3.7.
3. Count the number of places the decimal point was moved. Since the decimal point was moved one place to the right, the exponent for the power of 10 will be -1 (negative because the original number is less than 1).
4. Combine the coefficient and the power of 10 to write the number in scientific notation. The format is: ${3.7}^{-1}$.
5. Verify the result by converting the scientific notation back to standard form to ensure it matches the original number, 0.37.

Key Concepts

Scientific Notation

Scientific notation is a method of expressing numbers that are too large or too small in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 0.37 can be expressed as 3.7 x 10^-1, where 3.7 is the coefficient and -1 indicates the decimal place shift.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When converting to scientific notation, it is important to maintain the correct number of significant figures to accurately represent the original value.

Decimal to Scientific Conversion

Converting a decimal to scientific notation involves identifying the first non-zero digit and determining how many places the decimal point must move to place it immediately after this digit. This movement dictates the exponent of ten. For instance, moving the decimal in 0.37 one place to the right gives us 3.7, resulting in the scientific notation 3.7 x 10^-1.